Avoshifts

Ville Salo

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves all seven items of Theorem 1.1 for II-avoshifts on polycyclic groups via a general uniform-avo → uniform-SFT framework using the order-theoretic and constructibility properties of inductive intervals. The candidate gives an alternative, more constructive, axis-by-axis induction that assembles a finite window K_n and forbidden set P_n from top-axis determining sets and a well-founded "height" induction. While the model’s sketch omits some gluing details (how a local ‘decider’ at a boundary site is made compatible with the already-constructed interior) and implicitly assumes uniform determining sets for the canonical inductive intervals, these assumptions hold in the paper’s setting, and the gaps are patchable within the paper’s framework. Hence both establish the same results, by different methods.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper establishes a robust, order-theoretic framework (avoshifts on inductive intervals) that yields SFTness and basic algorithmic properties on polycyclic groups. The arguments are well-structured and, once the properties of inductive intervals are established, proceed cleanly to uniform SFT and safe computability. Some algorithmic sections remain at the level of safe procedures (as intended), and expanding a couple of constructive steps with a small example would improve clarity.